At 10:36 AM 4/24/04, Stathis Papaioannou wrote:
Does the fact that we never find ourselves in one of the bizarre, inconsistent worlds that are postulated to exist in Platonia cast doubt on the reality of these worlds and the validity of the underlying theory?

Not yet. We know that the bizarre, inconsistent worlds must exist if the Platonia idea is correct, but we (or at least I) don't currently know how likely they are. In Platonia, there are X number of possible-next-states from my current state. (For simplicity's sake, lets even say that X is a very very large finite number.) If a vast majority of these states show me sitting in my chair typing, with my computer not turning into a kangaroo, etc., then no, the fact that my world so far has not been bizarre and inconsistent does *not* cast doubt on the validity of the Platonia theory. In fact, if we can show logically, mathematically, or computationally (for me these are all ultimately the same thing) that a vast majority of my next-possible-states do in fact show me sitting in my chair typing, with very few computers turning into kangaroos, this would be an extremely strong reason to believe that the Platonia theory is correct, because it's survived a rather stringent falsification test.

Note that the tests we need to perform - tests like "how many of my next possible states show me still sitting in my chair? How many of my next possible states show my computer turning into a kangaroo?" - are logical / mathematical / computational ones, not empirical ones. We already have the empirical data, which we call "the laws of physics". We need to know what the Platonia theory actually predicts, and compare it to the empirical data. For my part, I don't actually know what the Platonia theory predicts, because I have no idea how to go about addressing the question mathematically. Bruno Marchal says we need to create a better model of what counts as a platonistic observer, and "interview it" about its relative consistent extensions (what I've been calling "next-possible-states"), and find out what regularities it would see. To me, that's just another statement of the problem. I don't have a very good model of what counts as a platonistic observer, and I don't know how to determine the structure of its next-possible-states, etc.

If we make progress on this issue, and we come to the mathematical conclusion that the probabilities we're looking for *don't* exist in Platonia - that is, if we determine that (say) my next-possible-states in which my computer turns into a kangaroo are just as common as those in which it remains a computer - then I think that that does cast doubt on the validity of the Platonia theory.

For your vacation, you buy a ticket that allows you to be destructively scanned and teleported to one thousand fabulous destinations around the solar system. The machine also sends a copy of you to a receiving station next door, on Earth (it's the rules). You enter the sending station, press the red button, and a second later find yourself in slightly altered surroundings. When you get out of the machine, you realise that you are still on Earth. Disappointed, you buy another ticket on the spot and go through the same procedure again, hoping for a better result. Again, however, you walk out and see that you are still on Earth. This time, you are angry. The probability that you finish up the stay-home copy twice is less than one in one million! You suspect on this basis that the company running the teleporter has cheated you, and did not send copies to the holiday destinations at all.

Your vacation-company thought-experiment brings up interesting issues about falsifiability. If I buy two tickets in a row, and I reappear on Earth both times, I'm tempted to suspect that I've been cheated. On the other hand, I know that the chances were 100% that this was going to happen to *some* copy. So maybe I'm just that unlucky copy? Unfortunately, if you continue to think in this way, you give up the idea of falsifiability completely. No matter how many times you buy a ticket and reappear on Earth, you can always argue that the chances were 100% that this would happen to some copy. No amount of empirical data can ever convince you that the company is cheating you. This is fine if you have some independent reason for trusting the company with 100% confidence, but without such an independent reason, you should suspect foul-play.

-- Kory

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